Free vibration analysis of a cylindrical micro-shell based on MCST

Abstract

Dynamic analysis of a functionally-graded (FG) cylindrical micro shell is investigated in this work. Effect of small parameter in micro scale is included in fundamental relations based on modified couple stress theory (MCST). For more precise analyzing the structure, third-order shear deformation theory (TSDT) is employed as kinematic relations. The shell is made from FG materials, using power function law. A solution procedure based on an analytical method is developed for special boundary condition. The numerical results are computed in graphical form to seek how changes of main parameters of the study such as micro parameter, in-homogeneity index and some geometric values change the free vibration responses. As an important output of this paper, it is concluded that an increase in micro parameter leads to increase of natural frequency. Furthermore, increase of in-homogeneous index yields more soft structure and then decrease of natural frequency.